After reading a variety of posts on what is wrong with sensor boats and what is right, the positives and negatives of diminishing returns, I feel that certain elements of the volumetric sensors provide opportunities, not just penalties. Note that certain of these ideas are highly-dependent upon others in the list.
Note that the first set of 4 ideas would take a lot of AI work to actually implement. The subsequent concept would not, and is a quick fix that still takes advantage of both radius and volumetric sensors.
1.) Sensors should be split between close-range, long-range, and targeting. A close-range sensor is your basic sensor package that lights up space around the ship, and maxes at one (note idea 3). The long-range sensors are the ones that are stacked on ships, and enable you to scan at greater distances around a ship; not just in all directions, but in a cone alternatively (if you're looking out towards a hostile frontier, you don't need half your sensors facing back towards home). This could be particularly valuable at enabling a fleet of ships to benefit from multiple sensor ships, as several ships could fill sensor gaps and increase the fleet's overall range (a minimum of long-range sensors would be required to actually scan outwards though). Then targeting and survey sensors would both enhance your accuracy in combat (note idea 2, with some form of either being essential on warships), with that being a fringe benefit for survey ships (so they don't need to waste sensor space). Targeting sensors would be a way of adding long-range sensor capacity to warships without it feeling utterly-pointless if they're matched in a fleet with normal sensor boats.
2.) Ships should require targeting sensors for combat. Even if sensors are left as-is, if a targeting sensor is needed for a ship to engage other warships effectively (with diminishing accuracy returns at a certain level, but bonuses against jamming or evasion), this would greatly reduce the problem that currently exists where the only logical ships to mount sensors on are pure sensor boats and survey ships. Given that jamming modules already exist which reduce accuracy, allowing ships to mitigate these problems with sensors would add practical value to attaching sensors to basic ships or using fleet-wide sensor modules.
3.) Add starting (i.e. free) modules to each ship. Each ship starts with some basic level of sensor range, engine power, life support, hit points, and tactical speed. This is based on the ship type and your researched empire bonuses. You should be able to switch these modules out for (limited selection) more or less-advanced variants, which will enable you to keep smaller ships competitive despite their smaller capacity (if you don't change anything, ships would effectively remain unchanged as they are now). This would enable ships to switch out whether they start with a generic close-range sensor or a targeting sensor (allowing you to use tiny ships as warships despite a sensor requirement). This would also enable you to reduce the cost of ships by mounting cheaper but less-efficient equipment.
4.) Add sensor stealth and cloaking. If long-range sensors and close-range sensors are differentiated, then you can set up a counter to sensor boats as cloaked ships sneak past 360-scanning long-range sensors, while sensor-stealthed ships sneak past long-range sensors being used to scan cones. Cloaks could eliminate the profile in generic scans, while ships with advanced sensors could focus their scans in a particular direction to potentially spot a cloaked ship (which would still have reduced profile, meaning the scan would have to be closer than normal); sensor stealth would conversely only have a reduced profile, meaning that slipping by the edge of the scan radius (which should be identifiable, since sensors typically send out as much energy as they pick up, i.e. active sonar; this also provides a converse option for passive sensors which don't send out emissions) would enable a sensor-stealthed ship to evade a sensor boat scanning long-distance in the same direction but lacking the sensor volume to properly cover the ship at its distance. Also, cloaked or sensor-stealthed ships would be harder to identify, making long-range readings on them (aka their size, armament, modules, etc) difficult to accurately identify.
Alternatively, just add sensor stealth, separate a single close-range sensor (radius-based) versus additional volumetric long-range sensors. If you can't scan everything in a direction, then you can pick how far out you want your ship to scan in a cone versus what radius you want for full-volume scans (basically, your ships can set a distance where the sensors only partially cover the space ahead, and you can pick how they scan). They could default to scan ahead of the ship, aim for unexplored space, rotate each move or each turn, or simply focus in a predetermined area (obviously needing to wait in order to actually shift). If the sensors are rotating and they identify a ship, but they are not fully covering it, then you would not get clear intel on what you spotted (maybe an unknown moniker spots up for a ship type, and you only know if it's armed, what faction, and what size it is). Either sensors would need to be pre-aimed at a direction, or you would need to get it into your 360-degree sensor radius to clearly identify the ship.
Basically, sensors covering volume instead of radius means you can actually ADD tactical depth by having multiple ships scan in directions, adding stealth tech, and adding a fog of war beyond pure invisibility to what exactly you are seeing. If a ship is at the bare edge of your sensor range, you shouldn't clearly identify what it is unless your basic (i.e. close-range) sensors are detecting it. The AI programming to add a stealth and tactical dimension would be more difficult, but at the very least, adding some fog-of-war rather than simply taking away sensor capabilities (and better yet, enabling radius-based sensors to still work in a rotating sonar-like system without actually identifying everything like universe satellites).